Unit 38Vectors

Presentation 1 Equal Vectors

Presentation 2 Components

Presentation 3 Vector Expressions

Presentation 4 Addition and Subtraction of Vectors

Presentation 5 Vector Geometry 1

Presentation 6 Vector Geometry 2

Unit 3838.1 Equal Vectors

In the following diagram, state

Which pairs of vectors are equivalent and which pairs of vectors are opposite directions

Equivalent vectors:a and b b and i f and g

Vectors in opposite directionsc and b e and j?

???

?

Unit 3838.2 Components

Does ?

?

?

?

?

Given that , , calculate

?

?

?

?

?

?

No

Unit 3838.3 Vector Expressions

Write down each of the following in terms of d and/or e.(a)

(b)

(c) ?

??

??

Mark clearly on the diagram(a) the point P such that(b) the point Q such that

Q

P

?

Unit 3838.4 Addition and Subtraction of

Vectors

Given that

On the grid below, illustrate the following vectors

(i) b – c(ii) c + a(iii) a + b(iv) a + c – b

b - c

- c

b

(i)

(ii)c + a

c

a

(iii)

a + b

ba

(iv) a + c - b

a + c - b

Unit 3838.5 Vector Geometry 1

Express, in terms of u and v,

(a)

(b)

(c) , where M is the midpoint of AC, ?

?

?

Express, in terms of u and v,

(d)

(e) , where N is the midpoint of BD,

(f)

?

?

? ?

?

What can you deduce about points M and N? They are coincident.

Hence and

Unit 3838.6 Vector Geometry 2

(a) Express in terms of x and y,(i) (ii) (iii)

Solution

In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that

(i)

(ii)

(iii) ??

?

?

?

In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that

(b) Show that

Solution

?

In the figure above, ABCD is a parallelogram such that and . The point P is on DB such that

(c) Given that E is the midpoint of DC, prove that A, P and E are collinear.

Solution

so

Hence A, P and E are collinear?

?

??

?

from part (b)

from part (a)